Online disinformation campaigns represent an increasingly serious threat to democratic societies. Although numerous tools have been developed to assist analysts in detecting and countering such operations, our comprehensive survey of the state of the art reveals persistent shortcomings in terms of coverage, interoperability, and explainability. To address these limitations, we first advocate a unifying conceptual framework that can serve as a semantic backbone. This framework harmonizes the heterogeneous outputs of existing tools and, in the longer term, supports the design of hybrid systems aligned with the principles of Explainable Artificial Intelligence (XAI). We then introduce a domain-specific Conceptual Data Model (CDM) that captures the strategic, structural, and behavioral dimensions of influence operations. Finally, we demonstrate the utility of this model through a real-world case study, illustrating how it enables a deeper and more transparent analyses of disinformation campaigns.